Despite bringing in Carlos Mac Allister and Dominik Szoboszlai to Anfield, Reds boss Jurgen Klopp remains keen on adding to his midfield options.
Klopp is a big admirer of Gravenberch and has been linked with the Bayern Munich throughout the transfer window so far.
The Dutchman however is not a player Liverpool are currently in the race to sign, according to Sky Deutschland.
Instead, Liverpool are focusing their efforts on Southampton midfielder Lavia, who is expected to cost in the region of £50m.
Lavia is also wanted by Arsenal and Chelsea, and if Liverpool lose out in the scrap for the 19-year-old, it remains to be seen if they will go back for Gravenberch.
The Dutchman is keen to make sure he is playing regularly next season after struggling during his first campaign in Bavaria.
Gravenberch, 21, clocked just 559 minutes of football in the Bundesliga as Bayern Munich won their eleventh straight league title.
